# [FieldTrip] Cluster-based permutation test - Help please :-)

emanuel vandenbroeke emanuelvandenbroeke at hotmail.com
Fri Jun 20 11:17:21 CEST 2014

```Dear Eric Maris,
On the website I found a solution for calculating the interaction effect with permutation testing!For my three way interaction I was thinking of the following solution and would like to know if this is statistically sound to do (perhaps also interesting for other people with the same design):
First I calculated the differences as proposed by you for an interaction effect, for each intensity separately:Thus:

T0
T1

Control arm
A
B

Intervention arm
C
D

B-A (with new variable difference_B-A) and C-D (with new variable difference_C-D). Instead of testing the interaction for these two new variables, I calculate the difference between variable difference_C-D and variable difference_B-A and use an F-statistic to express the differences across the 6 intensities and subsequently perform the permutation test.
Does this sound valid to you?I'm really stuck, so hope that you will answer my question!
Best wishes,Emanuel

From: emanuelvandenbroeke at hotmail.com
To: fieldtrip at science.ru.nl
Subject: Cluster-based permutation test
Date: Thu, 19 Jun 2014 14:11:31 +0200

Dear Eric Maris or other fieldtrippers,
In my experiment (a 2x2x6 design) I want to test whether ERP waveforms are significant different between conditions. There is no a priori assumption about the effects.In this experiment I apply a somatosensory stimulus on both arms before and after an intervention on one arm. The somatosensory stimulus consists of 6 different intensities. So it is a within-subject design with 3 factors: Time (T0 and T1), Arm (intervention, control) and Intensity (6 different intensities).
I'm interested in the MAIN effect of INTENSITY, and the INTERACTION effects (TIME x ARM) and (TIME x ARM x INTENSITY).For the Interaction effect TIME x ARM, I first calculated difference-waves (postcontrol - precontrol and postintervention - preintervention) in Matlab en then applied the permutation test on these difference-waves to test whether the two arms are different. I hope this is correct?
But now my question, how to test the TIME x ARM x INTENSITY interaction? One possibility might be to calculate an ANOVA F statistic for this interaction effect (so perform a full factorial ANOVA) and perform the permutation test? Is this justified?
Very much thanks,Best wishes,Emanuel

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